Lectures related to Dual Bases: Canonical and Dual Spaces

Linear Applications and Matrices

Delves into the bijection between linear applications and matrices, exploring linearity, injectivity, surjectivity, and the consequences of this relationship.

Linear Independence: Definition and Examples

Explores the concept of linear independence in vector spaces through definitions and illustrative examples.

Linear Forms in Vector Spaces

Covers the definition and properties of linear forms in vector spaces, including generating families and direct sums.

Linear Algebra Basics

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

Linear Transformations: Kernel and Image

Covers the concepts of kernel and image of a linear transformation and their relationship with the rank of the matrix.

Coordinate Systems and Applications

Covers the definition and use of coordinate systems and applications in bases and linear equations.

Diagonalization of Matrices and Least Squares

Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.

Linear Algebra Basics

Covers the basics of linear algebra, emphasizing the identification of subspaces through key properties.